A CHARACTERIZATION OF U4(2) BY NSE

Farnoosh Hajati, Ali Iranmanesh, Abolfazl Tehranian

DOI Number
https://doi.org/10.22190/FUMI1904641H
First page
641
Last page
649

Abstract


‎Let $G$ be a finite group and $\omega(G)$ be the set of element orders of $G$‎. ‎Let $k\in\omega(G)$ and $m_k$ be the number of elements of order $k$ in $G$‎. ‎Let $ nse(G)=\{m_k|k\in \omega(G)\}$‎. ‎The aim of this paper is to prove that‎, ‎if $G$ is a finite group such that nse($G$)=nse($U_4(2)$)‎, ‎then $G\cong U_4(2)$.

Keywords

element order; number of elements of the same order; projective special unitary group; simple Kn - group.

Full Text:

PDF

References


D. Chen : A characterization of PSU(3,4) by nse. International Journal of Algebra and Statistics 2 (2013), 51-56.

G. Frobenius: Verallgemeinerung des Sylowschen Satze. Berl. Ber. (1895), 981-993.

F. Hajati, A. Iranmanesh, and A. Tehranian: A characterization of projective special unitary group PSU(3,3) and projective special linear group PSL(3,3) by nse. Mathematics 6, no.7 (2018).

M. Herzog : On finite simple groups of order divisible by three primes only. J. Algebra 10, no.3, (1968), 383-388.

A. Iranmanesh, H. Parvizi Mosaed and A. Tehranian,: Characterization of Suzuki group by nse and order of group. Bull.Korean Math.Soc. 53, no. 3, (2016), 651-656, .

M. Jahandideh Khangheshlaghi and M. R. Darafsheh: Nse characterization of the Chevalley group G2(4). Arabian Journal of Mathematics 7 (2018), 21-26.

A. Khalili Asboei, S. S. Salehi Amiri, A. Iranmanesh, and A. Tehranian: A new characterization of A7,A8,. Anale Stintifice ale Universitatii Ovidius Constanta 21 (2013), 43-50.

A. Khalili Asboei, S. S. Salehi Amiri and A. Iranmanesh: A new characterization of Symmetric groups for some n. Hacettepe Journal of Mathematics and Statistics 43, (2013), 715-723.

A. Khalili Asboei, S. S. Salehi Amiri and A. Iranmanesh: A new note on characterization of a Mathieu group of degree 12. Southeast Asian Bulletin of Mathematics 38 (2014), 383-388.

A. Khalili Asboei : A new characterization of PSL(2,27). Bol. Soc. Paran. Mat. 32 (2014), no.1, 43-50.

A. Khalili Asboei, S. S. Salehi Amiri, A. Iranmanesh, and A. Tehranian: A characterization of sporadic simple groups by nse and order. J.Algebra and its Applications 12 (2013), no.2.

A. Khalili Asboei, S. S. Salehi Amiri, and A. Iranmanesh: A new characterization of PSL(2,q) for some q,. Ukrainian Mathematical Journal 67 (2016), no.9, 1297-1305.

M. Khatami, B. Khosravi and Z. Akhlaghi: A new characterization for some linear groups. Monatsh. Math. 163 (2011), no.1, 39-50.

S. Liu : A characterization of L3(4). Sci. Asia 39 (2013), 436-439.

S. Liu : A characterization of projective special unitary group U3(5) by nse. Arab Journal of Mathematical Sciences 20 (2014), no.1, 133-140.

S. Liu : A characterization of projective special linear group L3(5) by nse . Italian Journal of Pure and Applied Mathematics (2014), no.32, 203-212.

G. A. Miller : Addition to a theorem due to Frobenius,. Bull. Amer. Math. Soc. 11 (1904), no.1, 6-7.

H. Parvizi Mosaed, A. Iranmanesh and A. Tehranian: Nse characterization of simple group L2(3n). Publications De L’ institut Mathematique Nouvelle Serie 99 (2016), no.113, 193-201.

H. Parvizi Mosaed, A. Iranmanesh, M. Foroudi Ghasemabadi and A. Tehranian: A new characterization of simple group L2(2m),. Hacettepe Journal of Mathematics and Statistics 44 (2016), no.4, 875-886.

D. Passman: Permutation Groups. W.A. Benjamin, New York, 1968.

C. Shoa, W. Shi and Q. Jiang: Characterization of simple K4-groups,. Front. Math.China 3 (2008), no.3, 355-370.

C. Shoa, W. Shi, and Q. Jiang: A characterization of simple K3-groups. Advances in Mathematics 38 (2009), no.3, 327-330.

C. Shoa and Q. Jiang: A new characterization of some linear groups by nse. Journal of Algebra and its Applications 13 (2014), no. 2.

C. Shoa and Q. Jiang,: Characterization of groups L2(q) by nse where q ∈ {17, 27, 29}. Chin. Ann. Math. 37B (2016), no.1, 103-110.

R. Shen, C. Shoa, W. Shi, Q. Jiang, and V. Mazurov: A new characterization of A5, Monatsh. Math. 160 (2010), 337-341.

W. Shi: A new characterization of sporadic simple groups. In: Group Theory,(Proceeding of the 1987 Singapore Conference on Group Theory) Walter de Gruyter, Berlin 1989, pp. 531-540.




DOI: https://doi.org/10.22190/FUMI1904641H

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)